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Path Convergence and Approximation of Common Zeroes of a Finite Family of -Accretive Mappings in Banach Spaces

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  • Yekini Shehu
  • Jerry N. Ezeora

Abstract

Let be a real Banach space which is uniformly smooth and uniformly convex. Let be a nonempty, closed, and convex sunny nonexpansive retract of , where is the sunny nonexpansive retraction. If admits weakly sequentially continuous duality mapping , path convergence is proved for a nonexpansive mapping . As an application, we prove strong convergence theorem for common zeroes of a finite family of -accretive mappings of to . As a consequence, an iterative scheme is constructed to converge to a common fixed point (assuming existence) of a finite family of pseudocontractive mappings from to under certain mild conditions.

Suggested Citation

  • Yekini Shehu & Jerry N. Ezeora, 2010. "Path Convergence and Approximation of Common Zeroes of a Finite Family of -Accretive Mappings in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-14, August.
    • Handle: RePEc:hin:jnlaaa:285376
    DOI: 10.1155/2010/285376
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